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Two Fetish Fisting Blondes 2013 pornxn.com Water Pistols and SBR 2019 fetisheyes.com LezOnly Wetsuit Orgasms 2019 fetisheyes.com LezOnly Wetsuit Wrestling 2018 fetisheyes.com LezOnly Logic (from Greek: ??????, logik?, 'possessed of reason, intellectual, dialectical, argumentative')[1][2][i] is the systematic study of the forms of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments.[3] There is no universal agreement as to the exact definition and boundaries of logic, hence why the issue still remains one of the main subjects of research and debates in the field of philosophy of logic (see § Rival conceptions).[4][5][6] However, it has traditionally included the classification of arguments; the systematic exposition of the logical forms; the validity and soundness of deductive reasoning; the strength of inductive reasoning; the study of formal proofs and inference (including paradoxes and fallacies); and the study of syntax and semantics. A good argument not only possesses validity and soundness (or strength, in induction), but it also avoids circular dependencies, is clearly stated, relevant, and consistent; otherwise it is useless for reasoning and persuasion, and is classified as a fallacy.[7] In ordinary discourse, inferences may be signified by words such as therefore, thus, hence, ergo, and so on. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century). More recently, logic has been studied in cognitive science, which draws on computer science, linguistics, philosophy and psychology, among other disciplines. Contents 1 Types of logic 1.1 Informal logic 1.2 Formal logic 1.2.1 Mathematical logic 2 Concepts 2.1 Logical form 2.2 Semantics 2.3 Inference 2.4 Logical systems 2.5 Logic and rationality 2.6 Rival conceptions 3 History 4 Types 4.1 Syllogistic logic 4.2 Propositional logic 4.3 Predicate logic 4.4 Modal logic 4.5 Informal reasoning and dialectic 4.6 Mathematical logic 4.7 Philosophical logic 4.8 Computational logic 4.9 Non-classical logic 5 Controversies 5.1 "Is Logic Empirical?" 5.2 Implication: Strict or material 5.3 Tolerating the impossible 5.4 Rejection of logical truth 6 See also 7 References 7.1 Notes 7.2 Citations 7.3 Bibliography 8 External links Types of logic Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to capably think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry. Charles Sanders Peirce, First Rule of Logic Informal logic Informal logic is the study of natural language arguments. The study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, informal logic is not logic at all. (See § Rival conceptions.) Formal logic Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. In many definitions of logic, logical consequence and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.[8] Examples of formal logic includes traditional syllogistic logic (aka term logic); and modern symbolic logic: Syllogistic logic can be found in the works of Aristotle, making it the earliest known formal study. Modern formal logic follows and expands on Aristotle.[9][10] Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference,[11][12] often divided into two main branches: propositional logic and predicate logic. Mathematical logic Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and computability theory.[13][14] Concepts Argument terminology used in logic The concepts of logical form and argument are central to logic. An argument is constructed by applying one of the forms of the different types of logical reasoning: deductive, inductive, and abductive. In deduction, the validity of an argument is determined solely by its logical form, not its content, whereas the soundness requires both validity and that all the given premises are actually true.[15] Completeness, consistency, decidability, and expressivity, are further fundamental concepts in logic. The categorization of the logical systems and of their properties has led to the emergence of a metatheory of logic known as metalogic.[16] However, agreement on what logic actually is has remained elusive, although the field of universal logic has studied the common structure of logics. Logical form Main article: Logical form Logic is generally considered formal when it analyzes and represents the form of any valid argument type. The form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, to formalize simply means to translate English sentences into the language of logic. This is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a considerable variety of form and complexity that makes their use in inference impractical. It requires, first, ignoring those grammatical features irrelevant to logic (such as gender and declension, if the argument is in Latin), replacing conjunctions irrelevant to logic (e.g. "but") with logical conjunctions like "and" and replacing ambiguous, or alternative logical expressions ("any", "every", etc.) with expressions of a standard type (e.g. "all", or the universal quantifier ?). Second, certain parts of the sentence must be replaced with schematic letters. Thus, for example, the expression "all Ps are Qs" shows the logical form common to the sentences "all men are mortals", "all cats are carnivores", "all Greeks are philosophers", and so on. The schema can further be condensed into the formula A(P,Q), where the letter A indicates the judgement 'all – are –'. The importance of form was recognised from ancient times. Aristotle uses variable letters to represent valid inferences in Prior Analytics, leading Jan Lukasiewicz to say that the introduction of variables was "one of Aristotle's greatest inventions."[17] According to the followers of Aristotle (such as Ammonius), only the logical principles stated in schematic terms belong to logic, not those given in concrete terms. The concrete terms 'man', 'mortal', etc., are analogous to the substitution values of the schematic placeholders P, Q, R, which were called the 'matter' (Greek: ???, hyle) of the inference. There is a big difference between the kinds of formulas seen in traditional term logic and the predicate calculus that is the fundamental advance of modern logic. The formula A(P,Q) (all Ps are Qs) of traditional logic corresponds to the more complex formula {\displaystyle \forall x(P(x)\rightarrow Q(x))}{\displaystyle \forall x(P(x)\rightarrow Q(x))} in predicate logic, involving the logical connectives for universal quantification and implication rather than just the predicate letter A and using variable arguments {\displaystyle P(x)}P(x) where traditional logic uses just the term letter P. With the complexity comes power, and the advent of the predicate


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